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I have had this question in mind for a while, and I apologize if this is not the right forum to ask.

I am not referring to the description of piano tone, which is individual and of course highly subjective. Not being a scientist/engineer in this field, I am however interested to know whether there had been frequency analysis done on different piano's tone regarding relative composition/weight of overtones versus fundamentals.

I know a piano keystroke produces a complex response, and can be somewhat simplified to ADSR phases. I've heard in the A (attack) phase frequencies are chaotic, so I wonder whether there had been analysis on, say, the S (sustain) phase.

One of the reasons I am curious is that people often describe, categorically, that a certain brand's pianos emphasize more on the fundamentals (or vice versa). However, when I had the chance to try some of those makes (certainly very limited experience), I found all of them to be different. The thing is, none of those sounded close to what a tuning fork, supposedly the most pure fundamental, would sound.

I am not expecting a piano sound like a tuning fork, nor would I want that to happen.

Another example: Fazioli, a brand I haven't had the luxury to try, was often described to emphasize more on the fundamentals throughout its range. Yet all their models are designed to have tunable duplexes. If those duplexes are supposed to be tuned to allow for more sympathetic vibration, wouldn't that cause more overtones?

I don't know what publicly-available resources are available for acoustic pianos. I'm sure that the makers of "sample libraries" for sample-based software pianos have lots of knowledge, and guard it carefully. As do the makers of Pianoteq, a "modelled software piano" with several different-sounding "virtual pianos".

Some of the Pianoteq instruments have been developed with the cooperation of their acoustic-piano manufacturers. So (to calibrate the model for a specific piano) they must have done careful measurements of overtone structures, decay times, and so on.

For digital pianos, there's a long, rich thread called the "Digital Piano Bullshit Detector" in the Digital Piano forum:

https://www.pianoworld.com/forum/ubbthreads.php/topics/1365103/The_DPBSD_Project!.html#Post1365103

Much of that thread is devoted to the question:

. . . How close to "acoustic piano" can a DP get?

It is sleeping, now -- Dewster is busy earning a living with real projects.

Unfortunately, it doesn't have any _acoustic piano_ examples.

I did a Google search for "piano harmonic structure brand comparison" and found this collection of lectures on page 2 of the results (page 1 was mostly "sponsored" listings):


https://www.speech.kth.se/music/5_lectures/contents.html

Lecture 1 contents:



You might find it useful.

I wouldn't put too much stock in a precise meaning for the terms you referred to, there is no standard terminology for tone quality. I have heard people describe some pianos as emphasizing the fundamental, but to my ears they are full of much more upper partial energies than other pianos.

The best tone quality in my opinion is one that sounds warm and mellow when played soft but opens up with brilliance when played loud. Much like the voice of a skilled singer. Many pianos have reduced dynamics and tone color that does not change much with dynamics.

I suggest you ask the same question in the tuner and technician section here. There you will find kind souls who delight in such esoteric discussion.

Ian

Pianos do not have sustain, in the sense of ADSR.

Look for the work of ("Painted Post Dave") Dave Koenig on YouTube. Here is one link to get your started:

https://www.youtube.com/watch?v=7sfalZ_-EnY

Dave has probably done more work on analyzing piano sound than anyone else just now.

Del

Yes, Dave has posted many interesting examples of piano tone analyses using Matlab. In his work there are, for example, many graphical illustrations of the decay of relative partial strengths over time across the piano's scale for several different brands of pianos. I remember one example of where he tries to determine the characteristics of a European sound vs American sound by this means.

Here's an interesting read

https://smile.amazon.com/gp/product/0198722907

Thank you all for the great replies from which there are already a lot of interesting and substantial reads.

I think one thing that bugged me, when reading people talking about tones, was using terms of fundamentals and overtones. I fully appreciate subjective terms such as warm, bright, singing, "European" etc., descriptions that probably matter more musically, but as far as I know fundamentals and overtones are physical terms with clear definitions.